Finite Group Databasebeta

← C22×C17×#107 #14525914

Subgroups — C22×C17×#107 #14525914

Order 2176.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×C17C211yesmaximal, characteristic
2C22×C4⋊C4×C17C212yesmaximal
3C2×C17×#107C2112yesmaximal, direct product factor
4C23×C4×C17—22no—
5C23×C4×C17C2211yescharacteristic
6C22×C8×C17C418yescomplemented
7C22×C8×C17C2216yes—
8C2×C4⋊C4×C17—26no—
9C2×C4⋊C4×C17C22112yes—
10C17×#107C22116yesdirect product factor
11C24×C17D411yescharacteristic
12C22×C4×C17—212no—
13C22×C4×C17—48no—
14C22×C4×C17C2×C414yes—
15C22×C4×C17D413yes—
16C22×C4×C17Q814yes—
17C22×C4×C17C2313yes—
18C2×C8×C17C2×C4124yescomplemented
19C2×C8×C17C2314yes—
20C4⋊C4×C17—212no—
21C4⋊C4×C17C2318yes—
22C23×C17C4⋊C414yes—
23C23×C17D814yes—
24C23×C17Q1614yes—
25C23×C17C2×D413yes—
26C2×C4×C17—28no—
27C2×C4×C17—424no—
28C2×C4×C17C4⋊C4112yes—
29C2×C4×C17C22×C416yes—
30C2×C4×C17C2×D413yes—
31C2×C4×C17C2×Q816yes—
32C2×C4×C17C2411yescharacteristic
33C8×C17C22×C418yescomplemented
34C22×#107C1711yesmaximal, characteristic, direct product factor, Sylow
35C22×C17#107116yesdirect product factor
36C22×C17C2×C4⋊C416yes—
37C22×C17C2×D816yes—
38C22×C17C2×Q1616yes—
39C22×C17C22×D411yescharacteristic
40C4×C17—48no—
41C4×C17C2×C4⋊C416yes—
42C4×C17C23×C411yescharacteristic
43C4×C17C22×Q811yescharacteristic
44C23×C8C2×C1711yescharacteristic
45C22×C4⋊C4C2×C1712yes—
46C2×#107C2×C17112yesdirect product factor
47C2×C17C2×#107112yesdirect product factor
48C2×C17C22×C4⋊C411yescharacteristic
49C2×C17C22×D811yescharacteristic
50C2×C17C22×Q1611yescharacteristic
51C23×C4—22no—
52C23×C4C22×C1711yescharacteristic
53C22×C8C4×C1718yescomplemented
54C22×C8C22×C1716yes—
55C2×C4⋊C4—26no—
56C2×C4⋊C4C22×C17112yes—
57#107C22×C17116yesdirect product factor
58C17C22×#10711yescharacteristic, direct product factor, Sylow
59C24D4×C1711yescharacteristic
60C22×C4—212no—
61C22×C4—48no—
62C22×C4C2×C4×C1714yes—
63C22×C4D4×C1713yes—
64C22×C4Q8×C1714yes—
65C22×C4C23×C1713yes—
66C2×C8C2×C4×C17124yescomplemented
67C2×C8C23×C1714yes—
68C4⋊C4—212no—
69C4⋊C4C23×C1718yes—
70C23C4⋊C4×C1714yes—
71C23D8×C1714yes—
72C23Q16×C1714yes—
73C23C2×D4×C1713yes—
74C2×C4—28no—
75C2×C4—424no—
76C2×C4C4⋊C4×C17112yes—
77C2×C4C22×C4×C1716yes—
78C2×C4C2×D4×C1713yes—
79C2×C4C2×Q8×C1716yes—
80C2×C4C24×C1711yescharacteristic
81C8C22×C4×C1718yescomplemented
82C22C17×#107116yesdirect product factor
83C22C2×C4⋊C4×C1716yes—
84C22C2×D8×C1716yes—
85C22C2×Q16×C1716yes—
86C22C22×D4×C1711yescharacteristic
87C4—48no—
88C4C2×C4⋊C4×C1716yes—
89C4C23×C4×C1711yescharacteristic
90C4C22×Q8×C1711yescharacteristic
91C2C2×C17×#107112yesdirect product factor
92C2C22×C4⋊C4×C1711yescharacteristic
93C2C22×D8×C1711yescharacteristic
94C2C22×Q16×C1711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C17D4
commutatorC4C23×C4×C17
Frattini, cosocleC2×C4C24×C17
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C17 ◁ C23×C4×C17 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C17×#107C2direct (N × H)
6. C22×C8×C17C4semidirect
10. C17×#107C22direct (N × H)
18. C2×C8×C17C2×C4semidirect
33. C8×C17C22×C4semidirect
34. C22×#107C17direct (N × H)
35. C22×C17#107direct (N × H)
46. C2×#107C2×C17direct (N × H)
47. C2×C17C2×#107direct (N × H)
53. C22×C8C4×C17semidirect
57. #107C22×C17direct (N × H)
58. C17C22×#107direct (N × H)
66. C2×C8C2×C4×C17semidirect
81. C8C22×C4×C17semidirect
82. C22C17×#107direct (N × H)
91. C2C2×C17×#107direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C8×C172
C22×C4⋊C4×C172
C2×C17×#1072
C22×#10717